EP1566009B1 - Method of generating a stream cipher using multiple keys - Google Patents

Method of generating a stream cipher using multiple keys Download PDF

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Publication number
EP1566009B1
EP1566009B1 EP03757595A EP03757595A EP1566009B1 EP 1566009 B1 EP1566009 B1 EP 1566009B1 EP 03757595 A EP03757595 A EP 03757595A EP 03757595 A EP03757595 A EP 03757595A EP 1566009 B1 EP1566009 B1 EP 1566009B1
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EP
European Patent Office
Prior art keywords
function
byte
bytes
random number
key
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Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Expired - Lifetime
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EP03757595A
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German (de)
English (en)
French (fr)
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EP1566009A1 (en
Inventor
Stephen Laurence Boren
Andre Jacques Brisson
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/14—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using a plurality of keys or algorithms
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/06—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
    • H04L9/065—Encryption by serially and continuously modifying data stream elements, e.g. stream cipher systems, RC4, SEAL or A5/3
    • H04L9/0656—Pseudorandom key sequence combined element-for-element with data sequence, e.g. one-time-pad [OTP] or Vernam's cipher
    • H04L9/0662—Pseudorandom key sequence combined element-for-element with data sequence, e.g. one-time-pad [OTP] or Vernam's cipher with particular pseudorandom sequence generator
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/30—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
    • H04L2209/24—Key scheduling, i.e. generating round keys or sub-keys for block encryption

Definitions

  • the invention relates to the field of encryption methods and more particularly to a method of generating a stream cipher to encrypt electronic communications which may be extremely long.
  • OTP One-Time Pad
  • a OTP takes a stream of bits that contains the plaintext message, and a secret random bit-stream of the same length as the plaintext (the key).
  • OTP takes a stream of bits that contains the plaintext message, and a secret random bit-stream of the same length as the plaintext (the key).
  • To encrypt the plaintext with the key each pair of bits from the key and plaintext is sequentially acted on by the exclusive-or function to obtain the ciphertext bit.
  • the ciphertext cannot be deciphered if the key is truly random and the key is kept secret from an unauthorised party.
  • the problem with this method is that the key should be at least the same length as the message. If a shorter key is used and repeated then the cipher can be broken. In some cases the data which needs to be encrypted is extremely large.
  • US 4,058,673 discloses a method for generating a stream cipher having a length of x bits. i) A number n representing a number of sub-keys is selected. Furthermore, n unique relatively prime numbers mn each representing a unique sub-key length mn bits are selected. ii) N unique numbers are generated each having a length of mn bits. iii) A (n + 1) number R is generated. iv) For each bit which position is in said nth random number corresponds to p, where p ⁇ mn and p being a function of R, a function of each pth bit of each of said n random numbers is applied to generate a value. v) The value of p is incremented by one. vi) The steps iv) and v) are repeated and each value produced in step iv) is concatenated to the previous value produced in step iv) until the stream cipher of x bits in length has been produced.
  • the present invention provides a method and a computer program product according to the appended claims.
  • the invention further provides a computer program product for carrying out the method.
  • Fig. 2 illustrates by way of a flowchart the method of generating the encryption key of the present invention.
  • an encryption key a non-repeating stream cipher of indefinite length referred to herein as the Super Key
  • the Super Key is formed by combining sub-keys. Any number n of sub keys K 1 , K 2 , ..., K n can be specified depending on the application. The greater the number of sub-keys, the greater the length of the non-repeating Super Key.
  • the length of each sub key is a prime number of bytes (preferably with prime numbers larger than 10).
  • the first step in the process is to determine how large a Super Key, or stream cipher, to deploy.
  • the number n of sub-keys and the non-repeating length m n of each sub-key, in bytes, are selected.
  • the sub-keys each have a unique non-repeating length, that is, no two sub-keys are of the same non-repeating length.
  • the sub-key non-repeating lengths are prime numbers of bytes.
  • the length of the subkeys, in bytes are prime numbers in the range 2, 3, 5, ..., 1021, as there are 172 different prime numbers in this range.
  • the selection may be done by manually entering the number of sub- keys and their prime number non-repeating lengths.
  • the number of keys and their prime number non-repeating lengths is programmed into an application, or a program randomly selects the number of sub-keys and their non-repeating length.
  • the non-repeating length of the Super Key will be Size (K 1 ) X Size (K 2 ) X Size (K 3 ) ...X Size (K n ).
  • 10 sub- keys of the following prime number non-repeating lengths are used:
  • each of small prime number non-repeating length results in an extremely long non-repeating Super Key.
  • the total definition for the size of the Super Key above is contained in 300 bytes (the sum of the lengths of the non-repeating sub-keys) and the header (number of sub-keys and their lengths). Thus the total definition for a Super Key will be a fraction of the size of the Super Key.
  • each sub-key is a prime number of bytes, to improve the randomness of the resulting cipher, the method will also work if non-prime number lengths are used, as long as the resulting cipher is very large.
  • this is calculated by taking the first two digits generated by a random stream, MODed by 50 and adding 50 to provide a number of keys between 50 and 99.
  • Each sub-key of the multi-key process may be created as follows. First a random number which is not a perfect square is generated, preferably by a highly random source. Preferably it is an integer in the range of 500 to 700 digits. This serves as a "first seed value" O. It is verified that the selected value O is not a perfect square. If it is, then additional random values will be generated until one meets this criterion.
  • the second seed value is a 32-bit value that is used to seed the rand function of the computer. Random number generators that are included in the operating systems of most computers are pseudo-random and not very robust. These values, however, are sufficient as a starting point.
  • the second random number P is also generated from the computer's rand function.
  • the computer discards the digits in front of the decimal and computes the number Q up to P digits after the decimal. Then, starting at the Pth digit of Q after the decimal point, the computer sequentially selects 4 digits at a time, and calculates the Mod 256 value of the 4 digits. This results in an 8-bit value. This value is used as the first byte of the sub-key.
  • This process is repeated 4 digits at a time, continuing with the next digits in sequence, until a string of random data equal to the prime number non-repeating length of the sub-key being created is completed. This process is repeated for all the sub keys until the non-repeating length for all the sub keys are created. Each sub-key then is formed by taking the non-repeating string of bytes thus created, and repeating it as often as necessary to form a sub-key of sufficient length to create the Super Key in combination with the other sub-keys.
  • the Super Key (cipher) is created to the length required. This means the Super Key will continue to be created to encrypt the associated data to be encrypted, and continues to be created only until all the data is encrypted.
  • a random number R (“third seed value", or the starting offset for the Super Key, as opposed to the starting point P for the number Q) is generated.
  • the Modm n of R is calculated and the Modm n (R)th byte of each sub-key is consecutively exclusive-or'd (X/OR'd) with the corresponding Modm n (R)th byte of every other subkey.
  • the 3rd byte of sub-key 1 is selected and X
  • the process is repeated until all the selected bytes from each sub-key have been X/OR'd.
  • the resulting value may then be put through a substitution cipher or another delinearization function to delinearize the Super Key stream, as described further below.
  • the resultant binary value is then added to the Super Key by concatenation.
  • the next, subsequent byte of sub-key 1 is then X
  • the resulting binary value of each function is again added to the Super Key by concatenation. While the X/OR function is preferred, it will be apparent that other functions can be applied. For example, mathematical functions of addition or subtraction can be used.
  • the corresponding byte of the plaintext message is then encrypted with the corresponding byte of the Super Key by the exclusive-or function or some other mathematical function. Once all the bytes of the plaintext message have been encrypted the generation of the Super Key terminates.
  • the encrypted message can then be decrypted applying the inverse of the encrypting function to it and the Super Key.
  • ⁇ denotes the XOR operation.
  • Rmod l ⁇ i ⁇ returns an integer in the range 0,1,2,..., ( l ⁇ i ⁇ - 1)
  • the "SuperKey" has a j value that ranges from 0 to ((l ⁇ 1 ⁇ ⁇ l ⁇ 2 ⁇ ⁇ l ⁇ 3 ⁇ ... l ⁇ n ⁇ - 1).
  • an L-byte Super Key is generated, and a big number counter T is used to count the number of bytes in the plaintext.
  • the output is an L-byte ciphertext.
  • the same big number counter T is used and the output is the L-byte plaintext.
  • a further step may be applied to the Super Key before the plaintext message is encrypted.
  • a substitution cipher is applied to the Super key, and the resultant string is then used to encrypt the plaintext message.
  • an array of 256 unique bytes is created, from 1 to 256 ordered randomly. The first byte in the Super Key then has substituted for it the value of the x+1st byte in the Super Key, where x is the first value in the 256 byte array. The second byte in the Super Key then has substituted for it the value of the y+2nd byte in the Super Key, where y is the second value in the 256 byte array, and so on.
  • the 256-byte array can be formed from one of the sub-keys, plugging in bytes from a sub-key into the array so long as they don't repeat a previous entry in the array.
  • the linearity of the cipher text can be reduced also by applying the substitution cipher to the encrypted message (ciphertext) however it is more effective to apply the substitution cipher to the Super Key prior to encrypting.
  • Other utilities besides a substitution cipher can be used to break linearity, such as invertible non-linear function (INLF) utilities available from SANDIA labs. These are useful to provide protection against the Berlekamp-Massey attack.
  • ILF invertible non-linear function
  • the method will also work if the non-repeating string of each sub-key is simply generated by a random number generator to form each sub-key, as long as the overall resultant length of the Super key is sufficiently large so that the resultant Super Key is at least double the size of the data to be encrypted.
  • the foregoing method can be used to produce a personal security system whereby the key is used to encrypt personal files that the user wishes to secure. In that case no method of distribution of the key will be required.
  • a new file named ⁇ OLDFILENAME ⁇ OFFSET ⁇ ⁇ wn.
  • the OLDFILENAME includes the extension to allow for easy decryption and maintaining the same file format for functionality.
  • As each file is encrypted it is immediately decrypted and compared to the original and then both the test copy and the original file are deleted using a clean sweep deletion process (entire file rewritten as 0's and then 1's and then deleted).
  • a preferred key file format is defined as follows:
  • the foregoing key file format is standard. The only different value is the offset that is stored in a string of decimal digits that are delineated by "'s. An example of this would be "98-7654321", this allows for values ranging up to 1000 digits long which prevents the reuse of sections of the key stream if the offset is implemented properly.
  • the present invention is described above as a computer-implemented method, for example to encrypt and decrypt communications between computers 14 and 16 over network 12. It may also be embodied as a computer hardware apparatus, computer software code or a combination of same. The invention may also be embodied as a computer-readable storage medium embodying code for implementing the invention. Such storage medium may be magnetic or optical, hard or floppy disk, CD-ROM, firmware or other storage media. The invention may also be embodied on a computer readable modulated carrier signal.

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  • Engineering & Computer Science (AREA)
  • Computer Security & Cryptography (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Computing Systems (AREA)
  • Theoretical Computer Science (AREA)
  • Storage Device Security (AREA)
  • Signal Processing For Digital Recording And Reproducing (AREA)
  • Saccharide Compounds (AREA)
EP03757595A 2002-11-20 2003-10-06 Method of generating a stream cipher using multiple keys Expired - Lifetime EP1566009B1 (en)

Applications Claiming Priority (3)

Application Number Priority Date Filing Date Title
US10/299,847 US7190791B2 (en) 2002-11-20 2002-11-20 Method of encryption using multi-key process to create a variable-length key
US299847 2002-11-20
PCT/CA2003/001538 WO2004047361A1 (en) 2002-11-20 2003-10-06 Method of generating a stream cipher using multiple keys

Publications (2)

Publication Number Publication Date
EP1566009A1 EP1566009A1 (en) 2005-08-24
EP1566009B1 true EP1566009B1 (en) 2007-08-15

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EP03757595A Expired - Lifetime EP1566009B1 (en) 2002-11-20 2003-10-06 Method of generating a stream cipher using multiple keys

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US (1) US7190791B2 (zh)
EP (1) EP1566009B1 (zh)
JP (1) JP4608319B2 (zh)
KR (1) KR100994841B1 (zh)
CN (1) CN100568802C (zh)
AT (1) ATE370569T1 (zh)
AU (1) AU2003273688B2 (zh)
BR (2) BRPI0316473B1 (zh)
CA (2) CA2414261A1 (zh)
DE (1) DE60315700T2 (zh)
ES (1) ES2291675T3 (zh)
MX (1) MXPA05005358A (zh)
WO (1) WO2004047361A1 (zh)

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Also Published As

Publication number Publication date
AU2003273688B2 (en) 2009-06-25
ES2291675T3 (es) 2008-03-01
DE60315700D1 (de) 2007-09-27
EP1566009A1 (en) 2005-08-24
KR100994841B1 (ko) 2010-11-16
CN100568802C (zh) 2009-12-09
ATE370569T1 (de) 2007-09-15
BR0316473A (pt) 2005-10-11
CA2505338A1 (en) 2004-06-03
JP4608319B2 (ja) 2011-01-12
CA2505338C (en) 2012-09-04
BRPI0316473B1 (pt) 2018-03-13
KR20050086746A (ko) 2005-08-30
MXPA05005358A (es) 2005-08-03
DE60315700T2 (de) 2008-06-05
CN1714531A (zh) 2005-12-28
WO2004047361A1 (en) 2004-06-03
US20040096056A1 (en) 2004-05-20
US7190791B2 (en) 2007-03-13
AU2003273688A1 (en) 2004-06-15
CA2414261A1 (en) 2004-05-20
JP2006506668A (ja) 2006-02-23

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